Numerical Prediction of Propeller Induced Hull Pressure Pulses

THESIS FOR THE DEGREE OF LICENTIATE OF ENGINEERING

Numerical Prediction of Propeller Induced HullPressure Pulses

MUYE GE

Department of Mechanics and Maritime Sciences

CHALMERS UNIVERSITY OF TECHNOLOGY

Goteborg, Sweden 2019

Numerical Prediction of Propeller Induced Pressure Pulses

MUYE GE

© MUYE GE, 2019

Report no 2019:12


Chalmers University of Technology

SE-412 96 Goteborg

Sweden

Telephone + 46 (0)31-772 1000

Printed by Chalmers Reproservice

Goteborg, Sweden 2019

Numerical Prediction of Propeller Induced Hull Pressure Pulses

MUYE GE


Chalmers University of Technology

Abstract

Ship propeller induced pressure pulses is one of the major sources of both onboard

noise and vibration as well as underwater radiated noise. The need for accurate

pressure pulse prediction is increasing due to rising concerns of environmental

impacts and comfort and welfare of passengers and crews. More accurate pressure

pulse prediction is needed to be able to reduce the margin between high efficiency

propeller design and low pressure pulse propeller design.

Experimental approaches are used for pressure pulse assessments in the fi-

nal verification stage where models are produced, but they are limited in early

design work. Potential flow based methods have been used for early estimation

of pressure pulses, but due to the complexity of the pressure pulse generation

mechanisms, including interaction between hull and propeller and various types

of cavitation, viscous numerical methods are being developing as a complement to

potential flow method and a faster and cheaper alternative of experimental testing.

This thesis deals with the numerical prediction of marine propeller induced pres-

sure pulses adapted from typical experimental procedures, including both model

scale and full scale marine propellers operating in open-water conditions and be-

hind hull conditions with non-cavitating and cavitating flows. Simulations were

conducted using open-source package OpenFOAM and commercial package Star-

CCM+ with Reynolds-Averaged Navier-Stokes (RANS) method.

Studied cases show that for propellers in behind conditions, the present RANS

approach can provide good accuracy regarding 1st and 2nd order BPF (Blade Pass-

ing Frequency) hull pressure pulses early in design stage. Higher order BPF pres-

sure pulses were also predicted reasonably well, and different mechanisms in-

ducing higher order BPF pressure pulses, including small tip clearance, transient

cavitation appearance and sheet cavitation closure and its interaction with tip vor-

tex cavitation, are outlined in the thesis. For model scale propellers operating

under nearly uniform inflows, sheet cavitation is often over-predicted and an im-

proved cavitation mass transfer model is proposed which take laminar separation

as an additional inception criteria. Studies regarding mesh resolutions and scaling

effects are also included in certain cases.

Keywords: Pressure pulses, RANS, OpenFOAM, Star-CCM+, cavitation

iii

Acknowledgement

First of all, I would like to express my gratitude to my supervisor and examiner

Professor Rickard E. Bensow for his guidance and patience. I was granted a large

extent of freedom regarding research while when I am lost he always shows up

there and pointing out the right directions. I am also very grateful to my co-

supervisor Dr. Urban Svennberg, for his continuous support, encouragement and

valuable experiences shared.

In addition, I would like to thank Dr. Marko Vikstrom and Rikard Johans-

son for opening the door of research. Colleagues together at division of Marine

Technology provide a wonderful working environment. I would also like to ex-

press my gratitude to Johan Lundberg and Goran Grunditz for their support and

encouragement throughout the project.

The research project is funded by Kongsberg Maritime through Kongsberg

University Research Centre at Chalmers University of Technology. Simulations

were performed on resources at Chalmers Centre for Computational Science and

Engineering (C3SE) provided by the Swedish National Infrastructure for Com-

puting (SNIC).

v

List of appended publications

Two papers are appended in the present thesis:

• Paper I M. Ge, U. Svennberg, and R. E. Bensow. “Numerical Inves-

tigation of Pressure Pulse Predictions for Propellers Mounted on an In-

clined Shaft.” Proceedings of the Sixth International Symposium on Marine

Propulsors. Rome, Italy, 2019

• Paper II M. Ge, U. Svennberg, and R. E. Bensow. “Investigation on

RANS Prediction of Propeller Induced Pressure Pulses and Sheet-tip Cavi-

tation Interactions in Behind Hull Condition.” To be submitted.

vii

CONTENTS

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Related terminology . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.4 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Numerical modelling 11

2.1 Mass and momentum continuity equation . . . . . . . . . . . . . 11

2.2 Schnerr-Sauer cavitation model . . . . . . . . . . . . . . . . . . . 12

2.3 Laminar separation in the γ −Reθ model . . . . . . . . . . . . . . 13

2.4 Combination of laminar separation and cavitation . . . . . . . . . 14

2.5 Simulation Tools . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 Simulation results 19

3.1 Two high-skew propellers . . . . . . . . . . . . . . . . . . . . . . 19

3.2 A conventional container vessel . . . . . . . . . . . . . . . . . . 23

3.3 A general cargo vessel with LDP . . . . . . . . . . . . . . . . . . 32

4 Summary and future work suggestions 41

REFERENCES 45

ix

LIST OF FIGURES

1.1 Common types of cavitation on a marine propeller . . . . . . . . . 2

1.2 Pressure field induced by a breathing sphere source . . . . . . . . 5

2.1 The laminar separation indicator, upper frame: original prediction

based on γsep; lower frame: modified separation indicator. NACA

16012, AoA = 3 degrees, Re = 300,000, σ = atm. . . . . . . . . . 16

2.2 Numerical predicted cavitation patterns and separation indicator

at 0.002s (left column) and 0.1s (right column).From top to bot-

tom: predictions using original model; predictions using modified

model; separation indicator predicted by modified solver. NACA

16012, AoA = 3 degrees, Re = 1,000,000, σ = 0.045. . . . . . . . 16

3.1 Geometry and meshes of propeller A (left) and propeller B (right) 20

3.2 OpenFOAM results, 1st BPF pressure pulses, non-cavitating , pro-

peller A (left) and propeller B (right) . . . . . . . . . . . . . . . . 20

3.3 Predicted pressure pulse levels by different meshes, J = 0.85, non-

cavitating, propeller A . . . . . . . . . . . . . . . . . . . . . . . 20

3.4 Predicted cavitation pattern for propeller A with J = 0.85, σ = 2

by OpenFOAM (left) and Star-CCM+ (right) . . . . . . . . . . . 21

3.5 Cavitation patterns from high speed videos, propeller A, J = 0.85

and σ = 2; frame 1, 2, 3: snapshots from experimental recordings;

frame 4: numerical prediction using improved model . . . . . . . 21

3.6 Iso-surface of Q = 4e6, propeller A . . . . . . . . . . . . . . . . . 22

3.7 Laminar separation indicator with non-cavitating flow and J =0.85, propeller A with Tu = 5%, Tu = 0.5%, Tu = 0.1% and pro-

peller B with Tu = 0.1% . . . . . . . . . . . . . . . . . . . . . . 22

3.8 Pressure transducer arrangements on the model scale ship hull . . 23

3.9 Mesh close to the aft body . . . . . . . . . . . . . . . . . . . . . 24

xi

LIST OF FIGURES

3.10 Mesh view close to the propeller of base mesh; tip refined mesh

and closer view of tip refinement region. . . . . . . . . . . . . . . 24

3.11 1st (upper frame) and 2nd (lower frame) orders of BPF pressure

pulse levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.12 Predicted cavitation pattern and comparison with experimental

recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.13 Predicted iso-surfaces of α=0.5 and Q=1e7 for condition 1 with

tip refined mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.14 1st order BPF pressure pulse levels . . . . . . . . . . . . . . . . . 28

3.15 2nd order BPF pressure pulse levels . . . . . . . . . . . . . . . . 28

3.16 3rd to 5th orders BPF pressure pulse levels . . . . . . . . . . . . . 28

3.17 Non-dimensioned pressure history of probe 2 . . . . . . . . . . . 29

3.18 Cavity acceleration calculated based on recorded cavitation volumes 30

3.19 FFT result of equivalent pressure pulse based on d2Vtip/dt2 . . . . 30

3.20 Tip vortex collapse and rebounding . . . . . . . . . . . . . . . . . 31

3.21 Views of generated volume mesh . . . . . . . . . . . . . . . . . . 32

3.22 Arrangement of pressure transducers . . . . . . . . . . . . . . . . 33

3.23 Predicted thrust and torque coefficients for non-cavitating conditions 33

3.24 Pressure pulse levels at selected locations, non-cavitating condition 34

3.25 Predicted pressure fluctuation and Kp at probe No. 10 . . . . . . . 34

3.26 Effective wake at blade phase of 22.5 degrees under different con-

ditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.27 Comparison of sound pressure level at probe 10 . . . . . . . . . . 35

3.28 Pressure pulse levels on different probe points, cavitating condition 36

3.29 Cavitation patterns at blade phase of 22.5 degrees . . . . . . . . . 36

3.30 Predicted pressure fluctuations on probe 10, cavitating conditions . 37

3.31 Predicted thrust and torque coefficients for non-cavitating conditions 37

3.32 Predicted wave pattern . . . . . . . . . . . . . . . . . . . . . . . 37

3.33 Pressure pulse levels on different probe points, condition C . . . . 38

3.34 Predicted pressure fluctuations at probe 7 and probe 10 . . . . . . 38

3.35 Cavitation patterns predicted in condition C . . . . . . . . . . . . 39

xii

LIST OF TABLES

3.1 Summary of simulation conditions . . . . . . . . . . . . . . . . . 32

xiii

1Introduction

1.1 Background

Shipping is the most economical way of freight transportation and contributes to

the majority of world trade of cargo. As a major approach of ship propulsion,

marine propellers are widely used and propeller design with high propulsion ef-

ficiency is the major quest for propeller designers. However, there are several

side-effects generating design constraints including induced hull pressure pulses

and radiated noise which have been getting more attention in recent years.

The noise level in the ocean has increased about 3 dB every decade in the pe-

riod from 1950 to 2000 as reported in [1] as deduced from measurements recorded

in a measurement point in the Northeast Pacific Ocean. This number is equiva-

lent to the noise intensity level being doubled every ten years. According to more

recent statistics [2], the trend is not slowing down as the global ship density in-

creased about three times from 1990 to 2012. The impacts of ship radiated noise

for the environment and sea creatures are drawing more attention as well. In [3]

it has been found that the overlap between low frequency noise radiated by ma-

rine vessels and whale communication signals leads to a series of health hazard

for these sea mammals, and especially the noise in low frequencies ranging from

several propeller blade passing frequencies could travel as far as hundreds of kilo-

meters. The arctic transportation path is a new hot spot. The existence of ice

cover may change the propagation properties of generated noise and the impacts

to arctic environments can be another constraint.

High levels of on-board vibration and noise also impose health hazards to

the seafarers who are long-term exposed, including change of hearing sensitivity,

resonance in air containing organs, disorientation and acoustic annoyance [4].

Regulations like IMO Resolution MSC.337 addresses limits of on board noise

levels at different on-board areas according to exposure hours. The arising market

of cruise vessel and yacht also require noise and vibration levels below certain

1

1. Introduction

levels to maintain the comfort of passengers as the pressure fluctuation on the

hull body above propellers is one of the major sources of hull vibrations. The

prediction of under-water radiated noise usually relies on acoustic analogies which

are highly dependent on near-field pressure fluctuation predictions, and studies

show the high similarity between the two [5].

There are several major mechanisms influencing propeller induced pressure

pulses. As a propulsion unit, the propulsion force is generated by pressure differ-

ence on the opposite blade sides when the curved blades are rotating. The spatial

variation of blade position generate pressure variations and pressure waves to the

surrounding medium. Besides, the local pressure close to the propeller blades

might drop below saturation pressure where phase transfer from water to vapor

would occur, referred to as cavitation. The cavitation types for marine propellers

are classified according to the shape of different vapor structure, and the most

common ones are shown in figure 1.1: sheet cavitation, tip vortex cavitation and

bubble cavitation.

Figure 1.1: Common types of cavitation on a marine propeller

Experimental measurements are commonly used for propeller generated pres-

sure pulses studies. Several approaches have been developed to determine the

pressure pulse levels according to different types of configurations. Full scale

ship measurement could provide the most reliable values but it is usually difficult

to exclude the influences from sea states and due to the low transparency of sea

water and limitation of view angles the cavitation patterns can usually not be seen

clearly which could be vital for studies regarding pressure pulse generation. Be-

sides, it is usually desired to predict the pressure pulse levels before the real ship

is build. Experiments similar to Propeller Open-water Test (POT) could be con-

ducted inside the cavitation tunnel and in order to create load variation to mimic

2

1.1. Background

the working condition inside the ship wake, the propeller shaft is usually inclined

or meshes and plates could be applied upstream of the propeller. Furthermore,

the model scale ship hull could also be included in the cavitation tunnel, thus the

propeller would be operating in an actual model scale ship wake. An even more

challenging approach is to run the model scale ship with the propeller operating in

a towing tank which needs to be depressurized. In the cavitation tunnel, a higher

Reynolds number can usually be achieved which leads to a wake closer to full

scale ship and with less risk of laminar-transition flow. For the configuration in

a towing tank, usually Froude number similarity and cavitation number similar-

ity must be maintained while a major concern is that the flow Reynolds number

is usually even smaller than in a cavitation tunnel which might require special

treatments.

Cavitation, if present, is one of the major sources of induced pressure pulses,

however steady cavity structures are usually harmless regarding pressure pulses

including sheet cavitation and tip vortex cavitation [6]. Due to the fact that ma-

rine propellers are usually working in the ship wake, the propeller-hull interaction

plays an important role. The load on the propeller blade keeps changing while

changing position inside the wake and usually increases at the wake peak and the

induced pressure pulse would also increase locally. The cavitation structures are

also varying while the blade is rotating in the ship wake and might contribute

significantly regarding pressure pulse generation. The propeller induced pressure

pulses are quite in phase with blade rotation, thus the pressure pulse levels are

commonly shown in orders of blade passing frequency (BPF), and fast Fourier

transformation (FFT) is widely used to analyse pressure pulse signals in the fre-

quency domain.

It is believed that the 1st and 2nd order BPF fluctuations are caused by blade

thickness and load for non-cavitating conditions and growth/shrinkage of pro-

peller sheet cavitation for cavitating conditions. 3rd and higher order BPF pres-

sure pulses are believed to be originating from tip vortex cavitation related phe-

nomenon while the knowledge is still building on. In [7], a series of high skew

propeller models were studied experimentally in behind conditions and it was

found that the tip vortex cavitation contributes to pressure pulses ranging in be-

tween 3rd to 12th orders BPF. In [8], the model scale propeller E779A was studied

experimentally under non-uniform inflow and one of the deductions was that tip

vortex cavitation contributes mainly to the 3rd order BPF pressure pulse while

the leading edge cavity contributes to the 4th order BPF pressure pulse. More re-

cently, in [9], the tip vortex cavitation was found to increase pressure pulse levels

in the frequency range 400 hz to 2000 hz, which is approximately equivalent to

3rd to 13th orders BPF, and sheet cavitation, including its collapse and rebound,

mainly contributes to blade frequency as well as higher order BPF pressure pulses.

The tip vortex cavitation related phenomena were also found to be the source of a

broadband hump in the amplitude spectrum [9] and the other known contribution

to the hump is the cavitation differences between revolutions, which also reduces

the tonal at higher harmonics of BPFs according to experimental studies in [10].

3

1. Introduction

The ‘singing vortex’, termed in [11], was observed in experiments regarding cav-

itating foils which could cause significant increase of noise level and in [12] it

is deduced that strong excitation is a must for such phenomena. Furthermore,

the analytical model by Bosschers [13] and later studies [6] indicate that the ac-

tive pulsing source comes from tip vortex cavitation inside the wake. In [14], the

tip vortex bursting was found to be substantial in generating hull pressure pulses

and later, in [15], the tip vortex bursting was experimentally found to be signif-

icantly influenced by the wake which the propellers were operating in and this

phenomenon is referred to as sheet cavity closure in the studies in [16] where de-

veloped conceptual models of cavitation mechanisms regarding erosion including

interaction between sheet cavity and tip vortex cavitation. Besides, in [17], vari-

ous possible mechanisms were discussed regarding tip vortex cavitation induced

pressure pulses. The tip clearance between the propeller blade tip and hull is an-

other parameter that could be dominating in certain cases, as studied in [18]. The

interaction between tip vortex cavitation and the rudder could also be pronounced

as the tip vortex cavitation could become trapped in the gap between rudder and

hull and collapse thus inducing significant levels of pressure pulses, as noticed in

[19].

Numerical predictions of pressure pulses can be classified with increasing

computational cost as by empirical approach, potential flow based approach and

viscous flow based approach. For the potential flow based approach, Boundary El-

ement Method (BEM), lifting line method, lifting surface method and other tech-

niques can be found widely used. For the viscous flow based approach, RANS

(Reynolds-Averaged Navier-Stokes) and LES (Large Eddy Simulation) as well

as the combination between the two, DES (Detached Eddy Simulation) could be

commonly found. The potential flow based approach and viscous flow based ap-

proach could be used separately or together to balance computational cost and ac-

curacy. The empirical approach could also be used togehter with other approaches

and the blended approaches are referred to as semi-empirical approaches. Besides,

data driven models are also emerging [20].

RANS has been long used for marine applications including POT, resistance

test, wake prediction as well as self-propulsion test and many research studies

can be found using a RANS approach for pressure pulse predictions, including

[21, 22] for numerical pressure pulse predictions with similar configurations ac-

cording to POT and self-propulsion test. However, it is commonly regarded that

the RANS approach can only accurately predict pressure pulses up to 2nd BPF

due to the diffculties in tip vortex prediction. Scale resolved turbulence models

are used [23, 24, 25] for improved tip vortex predictions and in [26] numerical pre-

dictions using DDES were compared to full scale and model scale measurements.

LES and DNS are still too expensive for this kind of predictions. In [27], the

under-water noise generated by an operating propeller in behind condition using

wall-modelled Implicit LES was assessed and suggested that hundreds of million

cells would be needed to achieve anticipated resolution requirements. However,

it is still a promising method, as in [28] also the internal jets are predicted which

4

1.1. Background

could be another significant mechanism for pressure pulse formation. In [29],

more than one hundred million cells were used for tip vortex cavitation inception

predictions in POT-like conditions using ILES. In [30], the ILES was compared

with RANS regarding tip vortex predictions for a stationary foil and in [31], DNS

was applied in limited tip vortex zone and compared with RANS regarding tip vor-

tex predictions. In both studies RANS predicted generally a more diffusive tip vor-

tex but within limited distance downstream the foil, say around 5% ∼ 10% chord

length, the minimum pressure agreed well with experimental measurements.

From the acoustics point of view, acoustic sources can be classified into three

common types according to major modes of noise generation mechanisms: monopole,

dipole and quadrupole sources. Regarding marine propellers, the dipole sources

can be related with thickness noise (displacement of water medium) and load

noise (forces on propeller blades) while the quadrupole sources are typically re-

lated with flow turbulence. Monopole source generates pressure waves with den-

sity change due to changes in volume thus related to cavitation. As demon-

strated in figure 1.2, a breathing sphere with radius a and periodic surface veloc-

ity vAei(ωt−ka) would generate onmi-directional pressure waves to the surrounding

medium with density ρ0 , and together with the wave equation and the linearized

Bernoulli equation and neglecting density variation induced by acoustic waves,

the pressure at a location outside the sphere at a time p(r,t)could be derived as

p(r,t) =1

r

ρ0ωa2vA√1+(ka)2

ei(ωt−kr+arctan 1ka ). (1.1)

By introducing conditions r >> a and a << λ , the breathing sphere can be re-

garded as a point source and induced pressure fluctuation can be re-formulated as

the time derivative of volume flow rate QA and second order derivative of total

volume Vb regarding time, as shown in Equation 1.2.

p(r,t) = iωρ0

4πrQAeiω(t−r/c0) =

ρ0

4πr

∂QA(t − r/c0)

∂ t=

ρ0

4πr

∂ 2Vb(t − r/c0)

∂ t2. (1.2)

Figure 1.2: Pressure field induced by a breathing sphere source

5

1. Introduction

The similarity between second order derivative of sheet cavitation volume and

induced pressure pulses has been observed both experimentally and numerically

[32, 33] while especially in [33] the cavity volume was put equal to a moving

breathing sphere and estimated hull pressure pulses using the method of [34]. The

estimated value agreed well with hull pressure pulses measured by pressure trans-

ducer. In [7] it was found that the volume of pulsing tip vortex cavitation could be

related to the pressure pulse incidents in the time series recorded by hydrophones

and according to [13] and [6], the tip vortex cavitation generate pressure pulses in

a monopole manner when there are noticeably increasing noise levels.

1.2 Related terminology

The performance of a marine propeller is usually defined via non-dimensional

propulsion coefficients, i.e. advance ratio J, thrust coefficient KT , torque coeffi-

cient KQ and open water efficiency ηo. These coefficients are defined as shown in

Equation 1.3, in which VA represents inlet flow velocity, n represents propeller ro-

tation speed in rps, D represents propeller diameter, T represents propeller thrust,

ρ represents fluid density and Q represents propeller torque,

J =VA

nD, KT =

T

ρn2D4, KQ =

Q

ρln2D5

, ηo =JKT

2πKQ

. (1.3)

To achieve cavitation similarity in model scale experiments, the cavitation num-

ber should be equal to the full scale operating condition cavitation number. In

the present thesis the cavitation number σ is defined as Equation 1.4 for behind

conditions and as Equation 1.5 for open water conditions, which are based on the

pressure difference with saturation pressure pv with different reference values,

σ =p− pv

0.5ρl(πnD)2, (1.4)

σ =p− pv

0.5ρlV2A

. (1.5)

Pressure fluctuation p in model scale needs to be transformed to full scale, and

the scaling is based on the non-dimensional coefficient Kp, which is assumed to

be constant for model scale and full scale values. Kp is defined as,

Kp =p

ρln2D2

. (1.6)

The chord length at 0.75 blade radius cb are commonly used for blade Reynolds

number calculation when studying marine propellers,

Reb =cb

ν

√V 2

A +(0.75πnD)2. (1.7)

6

1.3. Research objectives

1.3 Research objectives

The research is focused on giving the scientific foundation for an engineering tool

for prediction of pressure pulses subjected to the ship hull above the propeller. As

pressure pulse induced noise and hull vibration are often required in contract to

be below a certain level, more accurate pressure pulse prediction would make it

possible to reduce the margin between high performance design and low pressure

pulse design.

Numerical simulation with RANS approach is a preferred engineering tool

which could provide more accurate predictions compared to BEM and less ex-

pensive than LES, thus selected to be the major simulation approach used in the

present study. The first objective is to investigate the capability and limitations

of the methodology in predicting hull pressure pulses aiming at 1st and 2nd blade

passing frequencies regarding the commonly used experimental configurations.

Ideally the non-dimensional coefficients in Section 1.2 are identical compar-

ing full-scale values and model-scale value. However, differences do exist which

are referred to as scale effects. Typically it is believed for a model scale pro-

peller with blade Reynolds number higher than 5× 105 - 1× 106, the scale ef-

fect is small regarding the force related propulsion coefficients but avoidance of

laminar-transition surface flow requires much higher Reynolds number [35]. The

assumption of similarity through equality of model scale cavitation number and

full scale cavitation number σm =σ f does not always hold true, especially for cav-

itation inception. The cavitation phenomena between model scale and full scale

are also influenced by scale effects, viscous effects and water quality. The influ-

ence of laminar-transition flow and Reynolds number difference between scales

regarding generated pressure pulses is the second objective to be investigated.

In order to achieve the research objectives, the following studies have been con-

ducted:

• Two high-skew propellers

Numerical simulations regarding two high-skew model scale marine pro-

pellers mounted on inclined shaft were performed and pressure pulses under

blade frequency were investigated. Simulations were conducted under dif-

ferent operating conditions J and cavitation numbers σ . Several meshes

were generated systematically and used to perform a mesh dependency

study. However, during the study massive sheet cavitation was predicted

by numerical simulations both in Star-CCM+ and OpenFOAM while in

the high speed videos recorded during experiments, these areas were only

covered by intermittent sheet cavitation strips or bubble cavities. The dis-

crepancies between cavitation patterns predicted numerically and observed

experimentally lead to a significant difference regarding pressure pulses.

Modifications of cavitation mass transfer model taking laminar separation

into consideration for sheet cavitation inception was made for prediction

7

1. Introduction

improvements.

• A conventional container vessel

The studied case is the container vessel designed and studied in the VIRTUE

and SONIC EU projects. In the experiments performed at HSVA, the model

scale ship hull was put into the cavitation tunnel test section, thus the pro-

peller was operating in the ship wake. Wake prediction was studied by sev-

eral generated meshes for the ship hull region. Two meshes with/without

blade tip refinement were considered to study tip vortex cavitation related

phenomenon. Besides, two sets of configurations based on different scaling

with different operating Reynolds numbers representing cavitation tunnel

condition and towing tank condition are numerically considered. Both Star-

CCM+ and OpenFOAM are used for all the simulated conditions as com-

parison and cross-reference. One of the research outputs from this study

that could be highlighted is that the re-entrant jet and side-entrant jet of

the sheet cavity plays an important role regarding the tip vortex cavitation

bursting phenomena. Based on the monopole nature of bursting tip vortex

cavitation, the isolated contributions of induced pressure pulses were stud-

ied which mainly concentrated in the BPFs ranging from 3rd order to 10th

order.

• A general cargo vessel with LDP

The third studied case is a general cargo vessel designed and studied in

the LeanShips EU project which attempts to acquire maximum propeller

efficiency by using a large diameter propeller incorporated by a new hull

design with significantly reduced tip clearance. The tip clearance is about

1% of propeller diameter, which is much smaller than the typical choice of

20% ∼ 30% of propeller diameter, and induced pressure pulse levels be-

came one of the major concerns to be taken care of. Both model scale and

full scale simulations are performed and the first four orders of BPF pressure

pulses are predicted and compared to experimental measurements. Besides,

the effect of hull roughness and free-surface are also studied.

For the cases that propeller is operating in behind condition, i.e. the container

vessel and the general cargo vessel with LDP, hull pressure pulses in orders higher

than 2nd BPF are predicted and discussions regarding various reasons of RANS

predicted higher order frequency pressure pulses are also included.

1.4 Thesis outline

The present thesis is divided into four parts. In Chapter 1, background infor-

mation is introduced including discussions regarding the research needs, pres-

sure pulse generation mechanisms, research methods, corresponding terminolo-

gies and research objectives.

8

1.4. Thesis outline

In Chapter 2, descriptions of related numerical formulations and methodolo-

gies are presented including simulation tools, basic control equations, mass trans-

fer cavitation model and transition sensitive turbulence model with its prediction

of laminar separation.

In Chapter 3, the summary of the studied cases are presented. The first pre-

sented case corresponds to the typical configuration of the model scale marine

propeller cavitation experiment and the pressure pulse induced by cavitation is

studied especially with improved numerical model which includes the effect of

laminar separation and sheet cavitation inception. The other two studied cases

are presented following which are the container vessel and the general cargo ves-

sel with LDP, while all of the two cases correspond to typical behind condition

experimental configurations.

Lastly the summary of the thesis and possible future work are presented in

Chapter 4.

9

1. Introduction

10

2Numerical modelling

2.1 Mass and momentum continuity equation

The basic control equations used in the present study are the mass and momentum

continuity equations, and their formulation in RANS for incompressible flow is,

∂ρm

∂ t+∇ · (ρmU) = 0, (2.1)

∂ρmU

∂ t+∇ · (ρmUU) = ∇ · (τ −ρmu′u′)−∇p+Fs, (2.2)

and the Boussinesq hypothesis is used for Reynolds stress tensor ρmu′u′ modeling,

−ρmu′u′ = µt(∇U+(∇U)T )−2

3ρmkI, (2.3)

where U represents time averaged velocity, u′ represents the time-varying fluctu-

ating component of velocity, µt is turbulent viscosity, Fs represents body forces,

ρm for mixture density, τ represents averaged stress tensor and I represents iden-

tity tensor. Turbulent viscosity is modelled using the kω −SST turbulence model

as µt = ρmkT where T represents turbulent time scale and k represents kinetic

energy. The turbulent time scale is calculated as min(a∗/ω,a1/SF2) in which

a∗,a1 are model constants, F2 is a blending function, S is the absolute value of the

strain rate and ω represents specific dissipation rate. Both k and ω are modelled

via additional Reynolds transport equations. The implementation of kω − SST

turbulence model in Star-CCM+ is based on [36] with S in the definition of the

eddy viscosity instead of the vorticity and furthermore, Durbin’s limiter in [37] is

used where both modifications concern the calculation of T . In OpenFOAM the

implementation is based on [38] with updated coefficients in [39].

Cavitation is one of the major sources of propeller induced pressure pulses.

The single fluid linear mixture approach is used for the present multi-phase prob-

11

2. Numerical modelling

lem. The two phases water and vapor are represented by a volume fraction factor

α which is between 0 and 1. Thus the mixture properties can be calculated as

ρm = αlρl +(1−αl)ρv, µm = αlµl +(1−αl)µv, αl +αv = 1,

in which the subscripts l and v represent liquid phase related quantities and vapor

phase related quantities. The transport equation of the volume fraction is written

as a pure convection equation with mass transfer source term for the liquid phase,

∂αl

∂ t+∇ ·αlU =

m

ρl

. (2.4)

2.2 Schnerr-Sauer cavitation model

In reality, rather than a perfect purified medium, water contains many small bub-

bles which can break the water medium when under tension. The small vapor

bubbles are commonly refered to as nuclei. The information of nuclei, including

the distribution of numbers and sizes, could be determined experimentally, and

usually it differs from test to test.

As indicated in 2.4, phase change is represented by a mass transfer source

term. There are many cavitation mass transfer models available, and the Schnerr-

Sauer cavitation model is one of the widely used models. For the study regarding

marine propeller cavitation, the differences between different phase change mod-

eling approaches are not significant [21]. In the Schnerr-Sauer cavitation model,

the distribution of nuclei are assumed to be spherical and uniformly distributed in

the water medium.

For uniformly distributed nuclei with diameter d and number n the volume in

one unit can be estimated as in Equation 2.5, thus the volume fraction of nuclei

can be expressed as in Equation 2.6 and bubble growth rates are estimated using

a simplified Rayleigh relation as shown in Equation 2.7,

Vnuc =1

6nπd3, (2.5)

αnuc =Vnuc

1+Vnuc

=16nπd3

1+ 16nπd3

, (2.6)

dR

dt=

√2

3

psat − p∞

ρl

. (2.7)

Accordingly the vapor production rate is calculated as,

dα

dt= (1−α)

4πnR2 dRdt

1+4πnR3/3. (2.8)

The mass transfer source term on the right hand side of Equation 2.4 can be further

re-organized as,

12

2.3. Laminar separation in the γ −Reθ model

m

ρl

=m

ρl

−αl(1

ρl

−1

ρv

)m+αl(1

ρl

−1

ρv

)m= (1

ρl

−αl(1

ρl

−1

ρv

))m+αl(1

ρl

−1

ρv

)m,

(2.9)

while the first term in Eq. 2.9 on the right hand side can be decomposed into two

terms (one for vaporization and one for condensation) as

mac =Ccαl

3ρlρv

ρmR

√2

3ρl

√1

|p− pthrehold|max(p− pthrehold,0),

mav =Cv(1+αnuc −αl)3ρlρv

ρmR

√2

3ρl

√1

|p− pthrehold|min(p− pthrehold,0).

Then the total rate of mass transfer is modified accordingly as

m = αlmav +(1−αl)mac = αl(mav − mac)+ mac. (2.10)

By introducing V = ( 1ρl−αl(

1ρl− 1

ρv)) and ∂ui

∂xi= ( 1

ρl− 1

ρv)m, the final transport

equation is written as,

∂αl

∂ t+∇ · (αlU) = (∇ ·U+Vv −Vc)αl +Vc. (2.11)

2.3 Laminar separation in the γ −Reθ model

The transition sensitive turbulence model, γ − Reθ model, is established based

on the Local Correlation based Transition Modeling (LCTM) concept [41]. The

model is based on empirical correlations and the used quantities are locally de-

termined for general usage of parallel computation. The model links the flow

transition characteristics (transition onset, length of transition, etc.) to flow fea-

tures (pressure gradient, free stream turbulence intensity level, etc.) based on

a series of two-dimensional experimental data. The model is coupled with the

kω − SST turbulence model with two additional equations. The first equation is

the intermittency equation, which controls the production of kinetic energy inside

the boundary layer; the second equation is a transport equation for transition mo-

mentum thickness Reynolds number, which is used to find the onset of transition

and takes the non-local empirical correlations, transfers them into local qualities.

Equation 2.12 displays the transport equation of intermittency γ , and Equation

2.13 the transport equation of momentum thickness Reynolds number Reθ t in

Cauchy format,

∂ (ργ)

∂ t+

∂ρU jγ

∂x j

= Pγ −Eγ +∂

∂x j

[(µ +

µt

σ f

)∂γ

∂x j

], (2.12)

13


∂ (ρReθ t)

∂ t+

ρU jReθ t

∂x j

= Pθ t +∂

∂x j

[σθ t(µ +µt)

∂ Reθ t

∂x j

], (2.13)

in which ρ denotes density, P and E are the production and destruction terms, µis the molecular dynamic viscosity, σ f and σθ t are model constants.

The foundation of this model is to use the correlation between scaled ratio of

vorticity Reynolds number Rev =ρy2

µ S and momentum thickness Reynolds num-

ber Reθ to represent the boundary layer shape factor H,

max(Rev)

2.193Reθ∼ H. (2.14)

Inside the boundary layer, y2S, the product of squared wall distance and strain rate

magnitude, can be regarded as the growth of disturbances, and the term µ/ρ can

be regarded as its damping. Transition will be triggered when a critical value of

Rev is reached.

Especially, the model is able of predicting laminar-separation induced transi-

tion. In a laminar boundary layer, with the increase of adverse pressure gradient,

the flow can be separating when shape factor H is higher than 3.5. Thus the scal-

ing constant in 2.14 is changed to 3.235 for better accuracy in between the target

shape factor range. In the original complete publication of the γ −Reθ model in

[40], the separation induced transition is formulated as

γsep = min(s1 max[0,Rev

3.235Reθc

−1]Freattach,2)Fθ t , (2.15)

in which s1 = 2,Freattach = e−(RT20 )

4and the blending function Fθ t is used to control

γSep is only active inside the boundary layer. Fθ t is equal to zero in the free stream

and one inside boundary layer, which is formulated as,

Fθ t = min(max(Fwake · e−( y

δ)4

),1.0− (γ −1/ce2

1.0−1/ce2)2,1.0), (2.16)

in which

θBL =˜Reθ t µ

ρU, δBL = 7.5θBL, δ =

50Ωy

U·δBL,

Reω =ρωy2

µ, Fwake = e−(Reω

1E5 )2

.

For the rest part of the model, the author refers to the publications in [41] and

[40] and in [42] for cross flow instabilities.

2.4 Combination of laminar separation and cavitation

Unlike for full scale propellers, where surrounding flow can be regarded as fully

turbulent, laminar and transitional flow is commonly found on blades of model

14

2.4. Combination of laminar separation and cavitation

scale propellers. As introduced in chapter 1, it is generally believed that with

Reynolds number higher than 1,000,000 the influence of laminar-transition effect

of propeller generated forces are small, but removal of laminar-transition surface

flow require way much higher Reynolds number [35]. Besides, many studies, in-

cluding [43, 44, 45, 46, 47], revealed that in most conditions the sheet cavitation

actually detach shortly downstream the location of laminar separation instead of

from the minimum pressure point, with some exceptions with detachment inside

the transition zone. At the same time, the problem is arising that there could

be large discrepancies of cavitation pattern between numerical predictions and

model scale experiments especially when operating under nearly uniform inflow

conditions. As shown in the two international workshops on cavitation and pro-

peller performance of International Symposium on Marine Propulsors [48, 49],

the problem of over-prediction of sheet cavitation under certain conditions was

found by different institute using various CFD packages, turbulence models, cav-

itation mass transfer models and nuclei properties in water medium.

In most Euler approach based cavitation mass transfer models, the sign of

(p− psat) is used as the only or major vaporization indicator as the vaporization

and condensation terms shown in section 2.2. Besides, one of the assumptions of

the Schnerr-Sauer mass transfer model is the uniform initial distribution of nuclei,

which is not true when the laminar boundary layer exists and nuclei may not

penetrate into the boundary layer as in turbulent boundary layers. The Lagrangian

method could be used to further study the problem as [50] regarding inceptions

from nuclei with different diameters while the transition sensitive model has also

been used to study the problem, including [51].

However, directly using transition-sensitive model do not really solve the prob-

lem as the predicted pressure distribution on the blades is hardly influenced, thus

similar cavitation patterns would be predicted as with the fully turbulent turbu-

lence models, even though the large area of laminar-transition region is predicted.

Linking between transition sensitive turbulence model and cavitation mass trans-

fer model is desired and the predicted laminar separation can be one candidate.

One developing approach here is to calculate a laminar separation indicator which

also multiples the two constants, Cc and Cv, which are the vaporization and con-

densation coefficients. This is somewhat desired since the two constants could

be modified according to the user; while taking into consideration the fact that

the laminar separation indicator would be modified to be one or zero, the original

properties of the cavitation model could be maintained as much as possible.

One feature of the vorticity Reynolds number based transition models is that

the transition always starts in the middle of the boundary layer, as γ and γsep in

Equation 2.15 increase locally and act as source terms of turbulent kinetic energy

k. The laminar separation indicator comes from γsep and fills the region between

the middle boundary layer and the wall. Experiments performed in [43] regarding

the NACA 16012 hydrofoil with 3 degrees angle of attack is used as a validation

case here. Figure 2.1 shows numerical predicted laminar separation regions. The

upper frame marks the region which satisfies Equation 2.15 while the lower frame

15


shows the modified separation indicator. The laminar separation could be found

about 0.78 chord length which agree well with experimental observation. For the

cavitating condition, numerical predictions using the original model (γ −Reθ and

Schnerr Sauer model) and the modified model (γ −Reθ and modified Cc and Cv

with SepInd in Schnerr Sauer model) are shown at inception time (T = 0.002s)

and developed time (T = 0.1s) as in figure 2.2. The inception of sheet cavity was

found from the foil rear part and moves upstream with the appearance of sheet

cavity, and finally an equilibrium state was found upstream foil mid chord. This

general behavior agrees well with experimental observations.

Figure 2.1: The laminar separation indicator, upper frame: original prediction

based on γsep; lower frame: modified separation indicator. NACA

16012, AoA = 3 degrees, Re = 300,000, σ = atm.

Figure 2.2: Numerical predicted cavitation patterns and separation indicator at

0.002s (left column) and 0.1s (right column).From top to bottom:

predictions using original model; predictions using modified model;

separation indicator predicted by modified solver. NACA 16012,

AoA = 3 degrees, Re = 1,000,000, σ = 0.045.

16

2.5. Simulation Tools

2.5 Simulation Tools

Two major packages are used in the present study, which are the open-source

package OpenFOAM and commercial package Star-CCM+. In both codes, the

set of equations is solved in a segregated manner, i.e. the equations of different

quantities are solved by sequence and iterations are needed until convergence. In

OpenFOAM, the solver interPhaseChangeFoam is used for two incompressible,

isothermal immiscible fluids with phase-change and transport equation of volume

fraction (TEM) is used to model the phases distribution. In the present study, a

modified code based on interPhaseChangeFoam implemented into OpenFOAM

v1806 is used. Simcenter Star-CCM+ is a complete multiphysics simulation tool

and in the present study the versions 11.06.010 and 12.06.010 were used. Same

as with OpenFOAM, for the presented simulated cases, the fluid is assumed to

be incompressible, isothermal immiscible and TEM is used for volume fraction

capturing. For simulations concerning water-air free surface, the VOF method is

used.

Throughout the simulations performed in the thesis, implicit second order up-

wind Euler scheme is used in both OpenFOAM (referred to backward) and Star-

CCM+ (referred to second order) while the implicit backward Euler with first

order accuracy, referred to as Euler in OpenFOAM and Euler implicit in Star-

CCM+, is used for simulation initialization for most cases. Gauss theorem is used

for the calculation of cell-centered gradient terms and convection terms as well

as Laplacian terms in OpenFOAM while in Star-CCM+ the calculation of gradi-

ent terms are hybrid with least-squares methods. Specificlly regarding gradient

calculation in OpenFOAM, linear interpolation scheme of face value is always

used without limiters while in Star-CCM+ the interpolation relies on reconstruc-

tion gradients with Venkatakrishnan limiter. Regarding convection flux calcula-

tion for term ∇ · (ρUU), interpolation of U f uses two schemes, where 2nd order

upwind differencing is the first one, denoted as linear upwind in OpenFOAM

and second order in Star-CCM+ while again in Star-CCM+ the reconstruction

gradient is used. A less diffusive TVD (Total Variation Diminishing) scheme

limitedLinear is also used for certain cases in OpenFOAM. First order upwind

scheme is used for turbulent terms and volume fraction factor α as suggested in

[52]. Pointwise is the major package for mesh generation while Star-CCM+ build-

in meshers might also be used if simulations are performed only in Star-CCM+.

Regarding pressure velocity coupling, the SIMPLE algorithm is always used for

steady-state simulations and transient simulations in Star-CCM+. In OpenFOAM

the PIMPLE algorithm is used for transient simulations.

17


18

3Simulation results

3.1 Two high-skew propellers

General description

In this study, two high-skew model scale marine propellers are considered. The

two propellers have similar designs and propulsion characteristics while one is

slightly more tip unloaded than the other one. Thus it is interesting to investigate

the design influence on the cavitation phenomenon and pressure pulses both ex-

perimentally and numerically. The geometries are shown in figure 3.1 including

surrounding grids.

Experiments were performed in the cavitation tunnel T31 at Kongsberg Hy-

drodynamic Research Centre at Kristinehamn, Sweden. The propeller shaft was

inclined about 10 degrees to create blade load variations. The propellers were

tested under different advance ratios and cavitation numbers. Eight pressure trans-

ducers were placed on the top wall of the cavitation tunnel test section above

the propeller to measure induced pressure pulse levels. High speed videos were

recorded for detailed study of related cavitation phenomenon. Experimental mea-

surements show that only the blade harmonic frequency pressure pulses are sig-

nificant and those in higher order harmonics are small enough to be neglected.

Numerical prediction and results comparison will be shown in the following sec-

tion and more details can be found in paper A.

19

3. Simulation results

Figure 3.1: Geometry and meshes of propeller A (left) and propeller B (right)

Results

Non-cavitating condition pressure pulses were numerically predicted and results

agreed well compared to experimental measurements both predicted by Open-

FOAM and Star-CCM+ using RANS with kω −SST turbulence model, as shown

in figure 3.2 and figure 3.3. A mesh study was performed using Star-CCM+ and

it shows the pressure pulse prediction for the current configuration is not highly

mesh dependent, since a mesh with a propeller region of 3.6 million cells (mesh

C in figure 3.3) predicted similar results compared to a 26.3 million cells mesh

(mesh OFF in figure 3.3).

Figure 3.2: OpenFOAM results, 1st BPF pressure pulses, non-cavitating , pro-

peller A (left) and propeller B (right)

Figure 3.3: Predicted pressure pulse levels by different meshes, J = 0.85, non-

cavitating, propeller A

20

3.1. Two high-skew propellers

However, for the cavitating conditions, massively over-predictions of sheet

cavitation could be found on both propellers and the predicted pressure pulses are

rather different compared to experimental measurements, not only absolute values

but also the spatial distributions on the transducers. As observed in the experi-

ments, for propeller A under condition J = 0.85 and σ = 2.0, the sheet cavitation

mostly develop at the tip leading edge, while traveling bubble cavitation could

form without any attached sheet cavitation. These typical patterns are shown in

figure 3.5. In the numerical predictions as shown in figure 3.4, the blade suction

side is covered by sheet cavitation which is clearly different from experimental

observations.

The arising problem that sheet cavitation might be over predicted has been dis-

cussed both in Chapter 1 and Chapter 2. By studying numerical simulations per-

formed by other researchers’ over-prediction results, the area of over-prediction

of sheet cavity is usually reflected as bubble cavitation observed in experiments.

The bubble cavitation reveals the fact that local pressure drops below saturation

pressure since certain nuclei could develop while for some reason sheet cavity

couldn’t develop on the blade surface. This type of isolated on blade bubble cav-

itation is not considered to appear in full scale, indicating this is a model scale

phenomenon.

Figure 3.4: Predicted cavitation pattern for propeller A with J = 0.85, σ = 2 by

OpenFOAM (left) and Star-CCM+ (right)

Figure 3.5: Cavitation patterns from high speed videos, propeller A, J = 0.85

and σ = 2; frame 1, 2, 3: snapshots from experimental recordings;

frame 4: numerical prediction using improved model

21


The transition sensitive turbulence model, γ − Reθ model was used to per-

form further investigation. For non-cavitating conditions, different free-stream

turbulence levels were considered and improved propulsion coefficients were pre-

dicted. Large regions of laminar-transition zone were predicted on the blade suc-

tion side and especially, series of near-wall streaky disturbances in the boundary

layer which triggers transition to turbulence were predicted, as shown in figure

3.6. These near-wall disturbances also indicate that the criteria Rev

3.235Reθc> 1 is

locally fulfilled as shown in figure 3.7. Though the predicted difference of thrust

coefficient differs up to about 4% between the kω − SST turbulence model and

γ − Reθ transition model, not much difference could be found regarding non-

cavitating conditions 1st BPF pressure pulse levels.

Thus the predicted separation indicator SepInd is linked to the cavitation

model as discussed in Section 2.4 and significant improvements could be found

regarding predicted cavitation patterns as shown in figure 3.5.

Figure 3.6: Iso-surface of Q = 4e6, propeller A

Figure 3.7: Laminar separation indicator with non-cavitating flow and J = 0.85,

propeller A with Tu = 5%, Tu = 0.5%, Tu = 0.1% and propeller B

with Tu = 0.1%

22

3.2. A conventional container vessel

3.2 A conventional container vessel

General description

This study focuses on the numerical prediction of cavitation and pressure pulse

induced by a model scale marine propeller operating in behind hull conditions.

The studied case is the container vessel used in the VIRTUE (The Virtual

Tank Utility in Europe) and SONIC (Suppression Of underwater Noise Induced

by Cavitation) EU projects. The container vessel is a representative 3600 TEU

standard container vessel developed in 2002 with a bulbous bow and single five-

bladed high skew fixed pitch propeller.

Experiments were performed in the cavitation tunnel HYKAT at HSVA, Ger-

many, which is large enough for the installation of the whole ship model. Pressure

fluctuations were measured at 13 probe points via pressure transducers mounted

on the ship hull above the propeller. The pressure transducer arrangements are

shown in figure 3.8.

Figure 3.8: Pressure transducer arrangements on the model scale ship hull

A mesh dependency study was performed first and comparison between different

meshes show that the wake is highly dependent on the ship hull mesh, especially

regarding prism cell layer generation. After the determination of ship hull mesh,

the behind-condition simulations including the propeller were carried out. Two

scaled model conditions were considered, where condition 1 corresponds to cav-

itation tunnel condition and condition 2 corresponds to a towing tank condition.

Two propeller meshes were considered with/without blade tip refinement in order

to investigate tip vortex related phenomena. Both OpenFOAM and Star-CCM+

were used for all the simulated conditions. The used meshes are shown in figure

3.9 and 3.10. More details can be found in the appended paper B.

23


Figure 3.9: Mesh close to the aft body

Figure 3.10: Mesh view close to the propeller of base mesh; tip refined mesh

and closer view of tip refinement region.

24


Simulation results

For non-cavitating conditions, the predicted pressure pulses and comparison with

experimental measurements are summarized in figure 3.11. The predicted model

scale pressure are scaled to full scale values where the Kp is calculated using

model scale values and Kp is assumed to be constant between different scales,

Kp =pm

ρmn2mD2

m

, ps = Kpρsn2s D2

s . (3.1)

The values are concentrated in the blade passing frequency and numerical pre-

dictions generally agree with experimental measurements. At some probe points

there are over-predictions of about 30% ∼ 40% but the maximum difference in

absolute value is small, about 0.4 kPa in full scale.

The predicted non-cavitating pressure pulse levels show very small differences

regarding the two operating conditions, though the Reynolds number differs about

3 ∼ 4 times. The prediction difference between the two numerical packages is also

very small, even though the numerical algorithms and discretization schemes are

not the same. Besides, using the tip refined mesh, much stronger tip vortex was

predicted, but there is little difference regarding predicted pressure pulse levels

compared to the predictions using the base mesh.

Figure 3.11: 1st (upper frame) and 2nd (lower frame) orders of BPF pressure

pulse levels

The prediction of cavitation patterns agree well compared to observations in the

experiments, including the convex shape of sheet cavity and its development as

well as sudden attenuated tip vortex cavitation with secondary structures predicted

by the tip refined mesh, though the stream-wise extent of the tip vortex cavitation

is weaker compared to experimental observations. The predicted cavitation pat-

terns and comparison to experimental recordings are shown in figure 3.12.

25


(a) 10 deg (b) 20 deg (c) 30 deg

(d) 40 deg (e) 48 deg (f) 58 deg

Figure 3.12: Predicted cavitation pattern and comparison with experimental

recording

Experimental recordings show that the sheet cavitation is the pronounced cavita-

tion phenomenon. The sheet cavity interface is sharp and clear while a convex

vapor structure could be found moving from the blade leading edge to the blade

trailing tip, originate at the blade position where the sheet cavity starts to form.

The sheet cavity decreases after blade position of 40 degrees. Around 40 to 48

degrees, coincident to the time when the convex vapor structure travels to the

blade tip end, the tip vortex cavitation starts to develop significantly and become

quite unstable and bursting with rather complex flow dynamics. After that, the tip

vortex cavitation is back to a relatively stable state around 58 degrees.

26


(a) 5.6 deg (b) 10.5 deg (c) 20.4 deg

(d) 29.5 deg (e) 35.2 deg (f) 40.1 deg

(g) 42.9 deg (h) 45.0 deg (i) 47.1 deg

(j) 49.9 deg (k) 54.8 deg (l) 64.7 deg

Figure 3.13: Predicted iso-surfaces of α=0.5 and Q=1e7 for condition 1 with tip

refined mesh

Transparent cavitation patterns together with the iso-surfaces of Q = 1× 107 for

condition 1 are shown in figure 3.13, to show the development of tip vortex, tip

vortex cavitation, sheet cavitation and their interactions. There is a jet flow formed

at about 0 degrees where the sheet cavity starts to develop, deduced from the

last frame (-7.3 degrees) and the first frame (5.6 degrees). Before the jet flow

reaches the tip region, say earlier than 30 degrees, the tip vortex is very stable

and limited tip vortex cavitation could be found developing. Then the secondary

vortex structures start form and the tip vortices, as well as tip vortex cavitation,

become quite active around blade phase of 48 degrees, which correspond to the

time when the jet flow arrives at the blade tip end. Instead of a main tip vortex

structure, the iso-surfaces of Q criterion show that the tip vortex is decomposed

into several rolling structures. The secondary structures starts to cavitate which

lead to a complex flow field.

27


The prediction of induced pressure pulse levels agree well for condition 1 in-

cluding satisfying predictions of 1st , 2nd and 3rd BPFs but over-predictions could

be found for the 4th and 5th BPFs. The higher order BPF pressure pulses levels

are around 0.5 kPa ∼ 1.0 kPa in experiments and 0.5 ∼ 2.5 kPa in numerical

predictions. The results are shown in figure 3.14 to figure 3.16. Differences were

found between the two scaled conditions and the major difference is the predicted

larger sheet cavitation extent which leads to higher 1st order BPF pressure pules

in condition 2.

Figure 3.14: 1st order BPF pressure pulse levels

Figure 3.15: 2nd order BPF pressure pulse levels

Figure 3.16: 3rd to 5th orders BPF pressure pulse levels

As shown in figure 3.17, the probed values of non-dimensional pressure (Kp) lo-

cated at transducer 2 in three blade passing period predicted using Star-CCM+

28


are presented for both base mesh and tip refined mesh under the two operating

conditions. The prediction results in condition 1 are plotted in black lines and red

lines are used for condition 2. The magnitudes of the predicted non-dimensional

pressure signals in condition 2 are larger than in condition 1 while the signal fluc-

tuations are of similar magnitudes. This is in accordance with the FFT results

that the 1st order BPF pressure pulses are larger in condition 2 while the values

are less influenced for the rest order of BPFs. The major events in the signals are

similar for one blade passing for the two operating conditions: starting from 0

degree, the signals decrease until about 30 degrees, after that a rapid increase and

decrease can be found which forms the first signal peak at around 40 degrees, then

follows the second peak at around 50 ∼ 60 degrees and lastly the signal decrease

with fluctuations and the signal repeats. For the pressure signals predicted using

the base mesh, the second pressure peak is absent and the first pressure peak is

stronger and ends earlier.

Figure 3.17: Non-dimensioned pressure history of probe 2

Vapor volumes were recorded during the numerical simulations as Vvapor =Σαv,iVi.

It is also of interest to isolate the vapor volume of the sheet cavitation and the tip

vortex cavitation, thus the cells with wall distance less than 2 cm, which covers

the sheet cavitation but excludes the tip vortex cavitation, are selected and the

vapor volume of these cells are computed as inner vapor volume. Taking sec-

ond derivatives over time of the recorded vapor volumes results in the vapor rate

shown in the first frame of figure 3.18. The resulting curves have highly similar

shapes compared to the pressure signals. It could be calculated that for this probe,

the pressure fluctuation is about p ∼ 2313.71×d2V/dt2. The calculated tip vor-

tex cavitation volume rate is shown in the second frame of figure 3.18, and the

deduced pressure pulse levels induced by TVC are calculated, as shown in figure

3.19. Taking advantage of the linear relationship, the vapor volume in the blade

tip region was isolated and this procedure indicates that the tip vortex cavitation

and the secondary cavitation structures induced pressure pulses up to 10th BPF.

The analysis of vapor volumes and pressure fluctuations provides a more com-

plete picture of the pressure pulse mechanisms for the present case, which is one of

the common types could be found in behind conditions. Starting from 0 degrees,

the present blade sheet cavitation extent increases until the total vapor volume

29


reaches its maximum at around 30 degrees. At the same time, the jet flows form

at around mid chord and travels to the blade tip. Then the sheet cavitation starts

to decrease in extent and pressure starts to increase. During this process the tip

vortex cavitation develops steadily. At about 40 degrees the jet flows reaches the

blade tip end, which leads to that a part of the sheet cavity collapses. After the

collapse, the pressure bounces back to relatively higher values, which is the first

pressure peak observed in the pressure signals. This event is less pronounced for a

tip refined mesh, due to the fact of tip vortex cavitation development. The blade tip

flow is influenced by the entrance of jet flows. Violent growth and collapse of tip

vortex cavitation could be observed between 48 degrees to 54 degrees, which lead

to the second pressure peak. After the second peak, the tip vortex cavitation shows

a monopole breathing manner and induce a series of fluctuations till about 82 de-

grees, added to the decreasing pressure signals. The tip vortex cavitation related

phenomenon generate pressure pulses in higher order BPFs, while the jet flow re-

lated sheet cavity collapse would lead to transient pressure fluctuations which is

another mechanism contributing to higher order BPF pressure pulses generation.

Figure 3.18: Cavity acceleration calculated based on recorded cavitation vol-

umes

Figure 3.19: FFT result of equivalent pressure pulse based on d2Vtip/dt2

The generation and collapse of tip vortex cavitation is repeated even outside the

wake peak, as shown in figure 3.20. Especially in the last four frames, at 73.4

degrees, the two tip vortex cavitation segments are collapsing, while the segment

30


between them are emerging at 75.5 degrees and 80.4 degrees and finally collapse

at 82.5 degrees. However, this phenomenon could not be observed in the experi-

mental recordings. In the experiments, the extent of tip vortex cavitation is contin-

uous and maintains its shape significantly further downstream, but the stretching

shape could be seen clearly.

(a) 53.4 deg (b) 58.4 deg

(c) 65.4 deg (d) 71.7 deg

(e) 73.4 deg (f) 75.5 deg

(g) 80.4 deg (h) 82.5 deg

Figure 3.20: Tip vortex collapse and rebounding

31


3.3 A general cargo vessel with LDP

General description

The studied case here is a ship with LDP (Large Diameter Propeller) designed

in the LeanShips (Low Energy And Near to zero emissions Ships) project. The

extremely low tip clearance (∼ 1%) makes a higher efficiency propulsion system

come true but clearly the effect of induced hull pressure pulse needs to be assessed.

Several conditions were considered in this study, as summarized in Table 3.1,

here named Condition A, B1, B2, and C. The model scale experiments were car-

ried out in the DWB (Depressurized Wave Basin) at MARIN (Maritime Research

Institute Netherlands) and induced pressure pulses were recorded via 14 pressure

transducers. The views of meshes are shown in figure 3.21 and the arrangement

of pressure transducers in figure 3.22.

Conditions Scale Free surface Wall roughness

A Model no Smooth

B1 Full no Smooth

B2 Full no Rough (120 micrometers)

C Full yes Rough (120 micrometers)

Table 3.1: Summary of simulation conditions

(a) Simulation domain for condition B (b) Volume mesh close to the forebody

(c) Free surface mesh for condition C (d) Propeller and aft-body surface mesh

Figure 3.21: Views of generated volume mesh

32

3.3. A general cargo vessel with LDP

Figure 3.22: Arrangement of pressure transducers

Simulation results

For conditions A, B1 and B2, the predicted non-cavitating thrust and torque co-

efficients are shown in figure 3.23. The match with experimental data is rather

satisfying for the thrust prediction, and the relative difference of predicted mean

thrust coefficients compared to experimental data are 1.2%, −2.5% and −0.1%

respectively. For the torque predictions, the relative difference of predicted mean

coefficients compared to experimental data are 4.9%, 1.6% and 3.1% respectively.

Figure 3.23: Predicted thrust and torque coefficients for non-cavitating condi-

tions

The predicted pressure levels for selected points in full scale for these non-

cavitating conditions are shown in figure 3.24. Together with probed pressure

fluctuation signals (scaled to Kp) in figure 3.25, it is found that the propeller suc-

tion side is responsible for transient pressure peaks and the transient peaks lead to

higher order components after FFT.

33


1st BPF pressure pulses 2nd BPF pressure pulses

3rd BPF pressure pulses 4th BPF pressure pulses

Figure 3.24: Pressure pulse levels at selected locations, non-cavitating condition

Figure 3.25: Predicted pressure fluctuation and Kp at probe No. 10

(a) Condition A (b) Condition B1 (c) Condition B2

Figure 3.26: Effective wake at blade phase of 22.5 degrees under different con-

ditions

The pressure pulse differences between conditions are directly related to the

wakes the propeller is operating in. The boundary layer is comparably thicker

34


in model scale than in full scale, while the hull roughness also leads to a thicker

boundary layer. The effective wakes under the conditions are shown in figure 3.26.

Together with the pressure signals in figure 3.25, it is found that the difference of

wakes mainly influence the predicted sharp pressure peak.

The Sound Pressure Level (SPL) are calculated for the recorded pressure sig-

nal from the model scale simulation (the grey line in figure 3.25 but unscaled), as

shown in Equation 3.2, and plotted in figure 3.27 with comparison to experimental

measurements at the same location. The local SPL is rich in higher order BPFs, as

the predicted pressure fluctuation contains very sharp peaks in each blade passages

and resulted similarly in a signal with repeated unit impulses, which includes all

frequencies.

Lp = 20log10(p

pre f

), pre f = 1µPa. (3.2)

(a) Experimental measurement (b) CFD model scale prediction

Figure 3.27: Comparison of sound pressure level at probe 10

The summary of pressure pulse levels for the cavitating conditions are shown

in figure 3.28, while the cavitation patterns in the experiment and simulations are

shown for blade phase of 22.5 degrees in figure 3.29. The cavitation number was

calculated based on full-scale ship operating condition at 0.75 propeller diameter

at the upper-most position with assumed wake height 0.75 m. Gravity was not

considered in condition A and B, to make the conditions comparable.

35




Figure 3.28: Pressure pulse levels on different probe points, cavitating condition

(a) Exp recording (b) Condition A

(c) Condition B1 (d) Condition B2

Figure 3.29: Cavitation patterns at blade phase of 22.5 degrees

The predicted pressure fluctuation signals on probe number 10 is shown in

figure 3.30. Compared to non-cavitating simulations, the pressure fluctuations

increased after each spike, due to the dynamics of cavitation. However, these

fluctuations are stronger in model scale than in full scale simulations. The pre-

dicted thrust coefficients and torque coefficients are summarized in figure 3.31.

The influence of cavitation on propeller propulsion performance is small.

36


Figure 3.30: Predicted pressure fluctuations on probe 10, cavitating conditions

Figure 3.31: Predicted thrust and torque coefficients for non-cavitating condi-

tions

The wave pattern predicted for condition C at the simulation time of 60s is

shown in figure 3.32. Some disturbances are found outside the Kelvin wave region

but the results are not expected to be influenced.

Figure 3.32: Predicted wave pattern

The predicted pressure pulse levels are summarized in figure 3.33. Same level

of accuracy was also obtained for cavitating conditions as non-cavitating condi-

37


tions, except the 2nd order BPF pressure pulses at probe point number 7, 11, 13

and 14. Generally the predicted results agree well with experimental data and the

differences between non-cavitating and cavitating condition are relatively small,

but at the mentioned probe locations the 2nd order BPF pressure pulses are over-

predicted, and the reason is not known. The pressure fluctuation history for probe

number 7 and 10 are plotted in figure 3.34. Comparing the two pressure signals,

similar variation in probe No. 7 as is observed in probe No. 10 is seen (both are

located close to each other on the center line of the hull above the propeller), while

the higher order harmonics are well predicted in probe No. 10.



Figure 3.33: Pressure pulse levels on different probe points, condition C

Figure 3.34: Predicted pressure fluctuations at probe 7 and probe 10

38


The predicted cavitation pattern at different blade positions are shown in fig-

ure 3.35. Cavity extent is slightly changed compared with the case B2, due to

both the changed hydrostatic pressure - as the wave elevation is different and that

for this case gravity is considered in the simulation - and the change in inflow

conditions - as boundary condition is of different shape compared with the double

body simulation of B2.

(a) Phase = 0 deg (b) Phase = 22.5 deg

(c) Phase = 45 deg (d) Phase = 67.5 and -22.5 deg

Figure 3.35: Cavitation patterns predicted in condition C

39


40

4Summary and future work suggestions

Summary

In the present thesis, numerical predictions of propeller induced pressure pulses

are presented and compared with available experimental measurements. The sim-

ulated conditions include model scale propeller mounted on inclined shaft, model

scale propeller operating in behind-hull condition, and full scale propeller operat-

ing in behind hull condition with and without free surface.

The first question is about the maturity of prediction of the present RANS

approach regarding 1st blade passing frequency pressure pulses. Generally speak-

ing the blade harmonic pressure pulses induced by a propeller in behind con-

ditions is shown to be reasonably predicted by the present RANS approach for

both non-cavitating and cavitating conditions. However, to maintain prediction

accuracy, the accurate prediction of the ship wake is of vital importance. The

difference could be up to 40% regarding 1st order BPF pressure pulse between a

well-resolved wake and a poorly resolved wake. The extent of sheet cavitation and

its variation can also be reasonably predicted. For the two Kongsberg high-skew

propellers operating under nearly uniform inflow conditions, numerical predic-

tion is rather different from experimental measurements and the prediction could

be misleading. Further studies reveals that the lack of sensitivity to laminar flow in

the cavitation mass transfer model could be the major reason and modified mod-

els were used for improved cavitation prediction by using a transition sensitive

turbulence model.

The second question is about the prediction ability regarding 2nd order and

higher orders BPF pressure pulse predictions. In the present study all the studied

cases in behind conditions the predicted pressure pulses are rich in higher order

BPFs including the 2nd order BPF. The studied cases revealed different mecha-

nisms inducing (numerical predicted) higher order BPF pressure pulses.

• For the general cargo vessel with LDP, the high order BPF pressure pulses

result directly from the very small tip clearance. Signal analysis shows that

41

4. Summary and future work suggestions

these high order components are not coming from tip vortex dynamics as

is normally argued, but from the short pressure peaks when the blade is

passing close to the hull. The short pressure peaks resulted similarly to a

signal with repeated unit impulses and FFT analysis of a this signal will

lead to high order components. Cavitation do not really excit higher values

of pressure pulses in this case. One reason is that the pressure peaks come

from the blade suction side while cavitation actually set lower limits of local

pressure to saturation pressure. The other reason is that the propeller is

rather lightly loaded, thus the cavitation volume is small and its variation is

not large sweeping by the hull surface.

• For the container vessel, higher order BPF pressure pulses were predicted as

well. The concluded reason is related to the sheet cavity closure, including

interactions between side-entrant jet and tip vortex as well as interactions

between sheet cavitation and ship wake. The starting of tip vortex burst-

ing is clearly related with the side-entrant jet and sheet cavity collapse, and

the tip vortex cavitation keeps rebounding outside the ship wake. The pres-

sure pulses generated by tip vortex cavitation is up to 10th BPF, as deduced

by the isolated vapor volume in the tip region. The study also verified the

fact that pulsing tip vortex cavitation is a monopole acoustic source. The

predicted results using the base mesh also reveals the fact that without re-

solving tip vortex cavitation, higher order BPFs pressure pulses would also

be predicted due to sheet cavity collapse.

Mesh spatial distribution is another topic here. In the present thesis the mesh

studies were conducted considering three aspects:

• Mesh study was performed for the Kongsberg high-skew propellers with

global refinement and the study revealed that for non-cavitating conditions

a rather coarse mesh could provide reasonable enough predictions.

• Mesh influence of bare hull wake prediction was investigated for the con-

tainer vessel case. For the case without free surface and appendages, 8

million cells seems to be a lower limit for boundary layer resolved mesh

with corresponding region refinements. The lack of the number of prism

layers may lead to an undesired transition ratio between last prism layer

cell height and core mesh size and a diffusive wake might be predicted.

• Another mesh related investigation is the tip refinement regarding tip vortex

cavitation predictions in the container vessel study. The base mesh and tip

refined mesh were both used and compared. Much more tip vortex cavita-

tion dynamics and higher order BPFs pressure pulses were predicted using

the tip refined mesh.

Scaling between different scales or Reynolds number is also investigated in

the present study. The major effective factor here is the wake influence regarding

42

blade load and sheet cavitation. For a higher Reynolds number scaled case, the

pressure pulses are typically lower due to the thinner boundary layer and more

compressed wake. This agree with observations in the literature though the influ-

ence of blade harmonic pressure pulse are generally smaller. Tip vortex and tip

vortex cavitation, which are known to be another highly Reynolds number depen-

dent phenomenon, are not included in the present study.

• In the study case of the general cargo vessel with LDP, simulations based

on model scale configurations and simulations based on full scale configu-

rations were performed and compared. The hull Reynolds number differs

about 150 times between the two and higher values of extrapolated pressure

pulses were predicted in model scale than in full scale. Tip vortex cavitation

related phenomenon are not studied in the present case.

• In the study case of the container vessel, simulations based on model scale

towing tank configurations and simulations based on model scale cavitation

tunnel configurations were performed and compared in which hull Reynolds

number differs about four times. Noticeable differences regarding sheet

cavitation extent were found between the two conditions as well as blade

frequency pressure pulse levels and small difference of tip vortex shape

could also be found.

Future work suggestions

As shown in the container vessel case in the present study, the generation/collapse

of tip vortex cavitation and the partial collapse of the sheet cavity, are the two ma-

jor events generating high values of pressure pulses and contribute to the higher

order BPFs. These two events are found to be highly dependent on the jet flows

inside the sheet cavitation. Early in year 2001, as studied by Kuiper [53], this very

common phenomena on ship propellers was discussed and the author pointed out

that ”knowledge of sheet cavitation cannot remain restricted to its outer surface”.

The jet flow has been widely studied on hydrofoils as re-entrant jet and for curved

bodies it can be related to the convex shape of sheet cavity closure line. The

present study shows that the ship wake may act as an important driving source

regarding the formation of the jet flows. The formation of the jet flow, its inter-

action with ship wake, blade geometry and sheet cavitation can be further studied

using more advanced approaches, which may provide fundamental knowledge of

this common phenomena.

It can be of interest to use more advanced approaches to resolve the tip vor-

tex cavitation in more details. The interaction with a more dynamic wake can be

of interest as well. However, by using the present RANS approach, the tip vor-

tex and tip vortex cavitation can be reasonably predicted within a short distance

downstream the blade tip which covers the region of sheet cavitation and tip vor-

tex cavitation interaction. Thus it may be more practical, as an engineering tool,

to combine the RANS predicted tip flow information with empirical approaches

43

4. Summary and future work suggestions

or theoretical tip vortex cavitation models, to include the contribution of tip vortex

cavitation for broadband pressure pulses.

Further study regarding laminar and transitional flow and sheet cavitation in-

ception is also of interest. The ships that have the needs to be assessed for pressure

pulses and radiated noises, are usually designed with low values of pressure pulses

and noise levels. For these cases the efficiency of propeller is less important and

usually the sheet cavitation and tip vortex cavitation become the primary phenom-

ena to be investigated. However, the over-predicted sheet cavitation in numerical

simulations may change the development of vortical structures on the blade tip

and prevent the formation of tip vortex cavitation. In order to match with ex-

periments, this effect should be treated properly. The combination of transition

sensitive turbulence model and mass transfer model seems to be an option but for

investigation of mechanisms more advanced approach is preferred.

Lastly, there is still a gap between model scale predictions and full scale val-

ues. This is not only concerning the scaling effects of ship wake and pressure

distribution on blades, but also concerning the differences regarding the mecha-

nisms of cavitation developments. Performing full scale simulations directly can

avoid some of the scaling effects, but as shown in the study in [54], the dynamics

of model scale simulation agree well with experimental data including tip vortex

cavitation dynamics, but the tip vortex cavitation was not captured in full scale

simulations. This indicates that full scale simulations seems to be restricted in

predicting tip vortex cavitation and high order BPF pressure pulses with moderate

computational resources nowadays.

44

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